Dynamics

Abstract

Derivation of the dynamic model of a manipulator plays an important role for simulation of motion, analysis of manipulator structures, and design of control algorithms. Simulating manipulator motion allows testing control strategies and motion planning techniques without the need to use a physically available system. The analysis of the dynamic model can be helpful for mechanical design of prototype arms. Computation of the forces and torques required for the execution of typical motions provides useful information for designing joints, transmissions and actuators. The goal of this chapter is to present two methods for derivation of the equations of motion of a manipulator in the joint space. The first method is based on the Lagrange formulation and is conceptually simple and systematic. The second method is based on the Newton-Euler formulation and allows obtaining the model in a recursive form; it is computationally more efficient since it exploits the typically open structure of the manipulator kinematic chain. The problem of dynamic parameter identification is also studied. The chapter ends with the derivation of the dynamic model of a manipulator in the operational space and the definition of the dynamic manipulability ellipsoid.